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This paper considers the problem of steering the state distribution of a nonlinear stochastic system from an initial Gaussian to a terminal distribution with a specified mean and covariance, subject to probabilistic path constraints. An…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
Motivated by applications arising from sensor networks and machine learning, we consider the problem of minimizing a finite sum of nondifferentiable convex functions where each component function is associated with an agent and a…
We present a collocated-grid framework for Direct Numerical Simulations of polydisperse particles submerged in a viscous fluid. The fluid-particle forces are coupled with the Immersed Boundary Method (IBM) while the particle-particle forces…
One of the main applications of the bound state in the continuum (BIC) is the low-threshold lasing. Ideally, the infinite quality factor of the BIC results in the zero-threshold and zero-linewidth lasing. However, various effects disturb…
Consider finitely many nets of multivariate c\`adl\`ag stochastic processes. We show that the vectors consisting of the respective minimizing points converge in distribution to a random closed set. This set is given as a cartesian product…
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…
Elastic similarity measures are fundamental to time series similarity search because of their ability to handle temporal misalignments. These measures are inherently computationally expensive, therefore necessitating the use of lower bounds…
A new notion of stochastic germs for quantum processes is introduced and a characterisation of the stochastic differentials for positive definite (PD) processes is found in terms of their germs for arbitrary Ito algebra. A representation…
Backpropagation (BP) is the most successful and widely used algorithm in deep learning. However, the computations required by BP are challenging to reconcile with known neurobiology. This difficulty has stimulated interest in more…
Two of the most popular parallel-in-time methods are Parareal and multigrid-reduction-in-time (MGRIT). Recently, a general convergence theory was developed in Southworth (2019) for linear two-level MGRIT/Parareal that provides necessary and…
Minimizing empirical risk subject to a set of constraints can be a useful strategy for learning restricted classes of functions, such as monotonic functions, submodular functions, classifiers that guarantee a certain class label for some…
We study the implicit bias of gradient flow on linear equivariant steerable networks in group-invariant binary classification. Our findings reveal that the parameterized predictor converges in direction to the unique group-invariant…
The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from…
The lattice Boltzmann method has become a widely adopted approach in computational fluid dynamics, offering unique advantages in mesoscopic kinetic modeling, intrinsic parallelism, and simple treatment of boundary conditions. However, its…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
Diffusions are a fundamental class of models in many fields, including finance, engineering, and biology. Simulating diffusions is challenging as their sample paths are infinite-dimensional and their transition functions are typically…
We establish a novel convergent iteration framework for a weak approximation of general switching diffusion. The key theoretical basis of the proposed approach is a restriction of the maximum number of switching so as to untangle and…